Question

please answer all of the following questions

18. On the day that his first child was bom, Ezio Auditore de Firenze deposited $6,200 into an investment account. The only purpose for the account was to pay for his son's first year of college tuition. Assume! that his son, Flavia, started college on his 18th birthday and his first year tuition payment had to be made that day. The amount needed on that day was $45,000. If that was indeed the amount of money in the account on Flavia's 18th birthday, what annual rate of return did Ezio earn on his investment account? 19. Marcus Holloway has $1,500 that he will use as a down payment on a car. Assuming that he can afford a payment of $225 per month, how much can Marcus spend on a car (that is, what is the total cost of the car that Marcus can purchase) if the interest rate is 5.75% and if he will finance his purchase with a 5 year, monthly payment loan? 20. Suppose Link deposits $5,000 into an account eaming 5 percent interest, compounded monthly. How many years (rounded to one decimal place - for example, 32.1843 year = 32.2) will it take for Links account to be worth $20,000?

Answer 1

Important Note: As per answering guidelines only the first question has been answered.

Solution- 18

The question requires us to calculate the Compounded Annual Growth Rate (CAGR) that Ezio earned on his investment. The formula for calculating CAGR is as follows:

CAGR= (FV/PV)^(1/n)-1

where,

FV= Future value of maturity value of investment ($45,000 as given in question)

PV= Initial investment ($6,200 as given in question)

n= No. of periods during which the investment got compounded (18 years as per question)

Therefore, putting the given values in CAGR formula, we get as follows:

CAGR= ($45,000/$6,200)^(1/18)-1

CAGR= (7.258065)^(0.556)-1

CAGR= 1.116409-1= 0.116409 or 11.64%

Therefore, the annual rate of return earned by Ezio during 18 year period is 11.64%